Topics in Quaternion Linear Algebra by Leiba Rodman (English) Hardcover Book

Description: Topics in Quaternion Linear Algebra by Leiba Rodman Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quate FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses or as a basis for a graduate course in linear algebra.The open problems can serve as research projects for undergraduates, topics for graduate students, or problems to be tackled by professional research mathematicians. The book is also an invaluable reference tool for researchers in fields where techniques based on quaternion analysis are used. Back Cover "This is a very serious treatise by an author who is a powerful researcher and a clear expositor. I know of no other book that treats both the basic theory and advanced material as carefully and as comprehensively as this one. Topics in Quaternion Linear Algebra is a singular contribution of considerable value." --Douglas R. Farenick, author of Algebras of Linear Transformations "This unique book brings under one cover various recent results obtained by Rodman, several of his collaborators, and other researchers. In addition to general topics in quaternionic linear algebra, it treats extensively the canonical forms of several types of quaternionic matrix pencils and the quaternionic numerical ranges of matrices. " --Dragomir Djokovic, distinguished professor emeritus, University of Waterloo Flap "This is a very serious treatise by an author who is a powerful researcher and a clear expositor. I know of no other book that treats both the basic theory and advanced material as carefully and as comprehensively as this one. Topics in Quaternion Linear Algebra is a singular contribution of considerable value." --Douglas R. Farenick, author of Algebras of Linear Transformations "This unique book brings under one cover various recent results obtained by Rodman, several of his collaborators, and other researchers. In addition to general topics in quaternionic linear algebra, it treats extensively the canonical forms of several types of quaternionic matrix pencils and the quaternionic numerical ranges of matrices. " --Dragomir Djokovic, distinguished professor emeritus, University of Waterloo Author Biography Leiba Rodman is professor of mathematics at the College of William & Mary. His books include Matrix Polynomials, Algebraic Riccati Equations, and Indefinite Linear Algebra and Applications. Table of Contents *FrontMatter, pg. i*Contents, pg. vii*Preface, pg. xi*Chapter One. Introduction, pg. 1*Chapter Two. The algebra of quaternions, pg. 9*Chapter Three. Vector spaces and matrices: Basic theory, pg. 28*Chapter Four. Symmetric matrices and congruence, pg. 64*Chapter Five. Invariant subspaces and Jordan form, pg. 83*Chapter Six. Invariant neutral and semidefinite subspaces, pg. 131*Chapter Seven. Smith form and Kronecker canonical form, pg. 153*Chapter Eight. Pencils of hermitian matrices, pg. 172*Chapter Nine. Skewhermitian and mixed pencils, pg. 194*Chapter Ten. Indefinite inner products: Conjugation, pg. 228*Chapter Eleven. Matrix pencils with symmetries: Nonstandard involution, pg. 261*Chapter Twelve. Mixed matrix pencils: Nonstandard involutions, pg. 279*Chapter Thirteen. Indefinite inner products: Nonstandard involution, pg. 300*Chapter Fourteen. Matrix equations, pg. 328*Chapter Fifteen. Appendix: Real and complex canonical forms, pg. 339*Bibliography, pg. 353*Index, pg. 361 Review One of Choices Outstanding Academic Titles for 2015 "Rodman fills a void in the monographic literature with this work."--Choice "The book is self-contained and well organized... Full and detailed proofs are supplied. Another exciting point is the presence of many open problems throughout the book."--Gisele C. Ducati, MatchSciNet Prizes Short-listed for Choice Magazine Outstanding Reference/Academic Book Award 2015 Review Quote "This unique book brings under one cover various recent results obtained by Rodman, several of his collaborators, and other researchers. In addition to general topics in quaternionic linear algebra, it treats extensively the canonical forms of several types of quaternionic matrix pencils and the quaternionic numerical ranges of matrices. " --Dragomir Djokovic, distinguished professor emeritus, University of Waterloo Details ISBN0691161852 Author Leiba Rodman Publisher Princeton University Press Series Princeton Series in Applied Mathematics Year 2014 ISBN-10 0691161852 ISBN-13 9780691161853 Format Hardcover Imprint Princeton University Press Place of Publication New Jersey Country of Publication United States DEWEY 512.5 Pages 384 Media Book Short Title TOPICS IN QUATERNION LINEAR AL Language English Translated from English Series Number 45 UK Release Date 2014-08-24 Publication Date 2014-08-24 NZ Release Date 2014-08-24 US Release Date 2014-08-24 Audience Tertiary & Higher Education AU Release Date 2014-11-02 We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:137779442;

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